Results 1  10
of
14
Energy Efficient Routing in Ad Hoc Disaster Recovery Networks
, 2003
"... The terrorist attacks on September 11, 2001 have drawn attention to the use of wireless technology in order to locate survivors of structural collapse. We propose to construct an ad hoc network of wireless smart badges in order to acquire information from trapped survivors. We investigate the energy ..."
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The terrorist attacks on September 11, 2001 have drawn attention to the use of wireless technology in order to locate survivors of structural collapse. We propose to construct an ad hoc network of wireless smart badges in order to acquire information from trapped survivors. We investigate the energy efficient routing problem that arises in such a network and show that since smart badges have very Hmited power sources and very low data rates, which may be inadequate in an emergency situation, the solution of the routing problem requires new protocols. The problem is formulated as an anycast routing problem in which the objective is to maximize the time until the first battery drainsout. We present iterative algorithms for obtaining the optimal solution of the problem. Then, we derive an upper bound on the network lifetime for specific topologies. Finally, a polynomial algorithm for obtaining the optimal solution in such topologies is described.
FlowCut Gaps for Integer and Fractional Multiflows
, 2009
"... Consider a routing problem instance consisting of a demand graph H = (V, E(H)) and a supply graph G = (V, E(G)). If the pair obeys the cut condition, then the flowcut gap for this instance is the minimum value C such that there exists a feasible multiflow for H if each edge of G is given capacity C ..."
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Cited by 9 (1 self)
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Consider a routing problem instance consisting of a demand graph H = (V, E(H)) and a supply graph G = (V, E(G)). If the pair obeys the cut condition, then the flowcut gap for this instance is the minimum value C such that there exists a feasible multiflow for H if each edge of G is given capacity C. It is wellknown that the flowcut gap may be greater than 1 even in the case where G is the (seriesparallel) graph K2,3. In this paper we are primarily interested in the “integer ” flowcut gap. What is the minimum value C such that there exists a feasible integer valued multiflow for H if each edge of G is given capacity C? We formulate a conjecture that states that the integer flowcut gap is quantitatively related to the fractional flowcut gap. In particular this strengthens the wellknown conjecture that the flowcut gap in planar and minorfree graphs is O(1) [12] to suggest that the integer flowcut gap is O(1). We give several technical tools and results on nontrivial special classes of graphs to give evidence for the conjecture and further explore the “primal ” method for understanding flowcut gaps; this is in contrast to and orthogonal to the highly successful metric embeddings approach. Our results include the following: • Let G be obtained by seriesparallel operations starting from an edge st, and consider orienting all edges in G in the direction from s to t. A demand is compliant if its endpoints are joined by a directed
Approximate maxintegralflow/minmulticut theorems
, 2004
"... We establish several approximate maxintegralflow / minmulticut theorems. While in general this ratio can be very large, we prove strong approximation ratios in the case where the minmulticut is a constant fraction ɛ of the total capacity of the graph. This setting is motivated by several combina ..."
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Cited by 6 (2 self)
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We establish several approximate maxintegralflow / minmulticut theorems. While in general this ratio can be very large, we prove strong approximation ratios in the case where the minmulticut is a constant fraction ɛ of the total capacity of the graph. This setting is motivated by several combinatorial and algorithmic applications. Prior to this work, a general maxintegralflow / minmulticut bound was known only for the special case where the graph is a tree. We prove that, for arbitrary graphs, the maxintegralflow / minmulticut ratio is O(ɛ −1 log k), where k is the number of commodites; for graphs excluding a fixed subgraph as a minor (for instance, planar graphs), O(1/ɛ); and, for dense graphs, O(1 / √ ɛ). Our proofs are constructive in the sense that we give efficient algorithms which compute either an integral flow achieving the claimed approximation ratios, or a witness that the precondition is violated.
Algorithms for 2Route Cut Problems
, 2008
"... In this paper we study approximation algorithms for multiroute cut problems in undirected graphs. In these problems the goal is to find a minimum cost set of edges to be removed from a given graph such that the edgeconnectivity (or nodeconnectivity) between certain pairs of nodes is reduced below ..."
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Cited by 5 (0 self)
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In this paper we study approximation algorithms for multiroute cut problems in undirected graphs. In these problems the goal is to find a minimum cost set of edges to be removed from a given graph such that the edgeconnectivity (or nodeconnectivity) between certain pairs of nodes is reduced below a given threshold K. In the usual cut problems the edge connectivity is required to be reduced below 1 (i.e. disconnected). We consider the case of K = 2 and obtain polylogarithmic approximation algorithms for fundamental cut problems including singlesource, multiwaycut, multicut, and sparsest cut. These cut problems are dual to multiroute flows that are of interest in faulttolerant networks flows. Our results show that the flowcut gap between 2route cuts and 2route flows is polylogarithmic in undirected graphs with arbitrary capacities. 2route cuts are also closely related to wellstudied feedback problems and we obtain results on some new variants. Multiroute cuts pose interesting algorithmic challenges. The new techniques developed here are of independent technical interest, and may have applications to other cut and partitioning problems.
1 Optimal Scaling of Multicommodity Flows in Wireless Ad Hoc Networks: Beyond The GuptaKumar Barrier
"... Abstract—We establish a tight maxflow mincut theorem for multicommodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cutcapacity scale as Θ(n 2 r 3 (n)/k) for a random choice of k≥Θ( ..."
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Abstract—We establish a tight maxflow mincut theorem for multicommodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cutcapacity scale as Θ(n 2 r 3 (n)/k) for a random choice of k≥Θ(n) sourcedestination pairs, where r(n) is the communication range in the network. We exploit the fact that the MCF in a random geometric graph equals the capacity of an adhoc network under the protocol model and interferencefree communication to derive scaling laws for interferenceconstrained network capacity. We generalize all existing results reported to date by showing that the percommodity capacity of the network scales as Θ(1/r(n)k) for the singlepacket reception model suggested by Gupta and Kumar, and as Θ(nr(n)/k) for the multiplepacket reception model suggested by others. More importantly, we show that, if the nodes in the network are capable of multiplepacket transmission and reception, then it is feasible to achieve the optimal scaling of Θ ` n 2 r 3 (n)/k ´ , despite the presence of interference. This result provides an improvement of Θ ` nr 2 (n) ´ over the highest achieved capacity reported to date. In stark contrast to the conventional wisdom that has evolved from the GuptaKumar results, our results show that the capacity of adhoc networks can actually increase with n while the communication range tends to zero! I.
Chromatic characterization of biclique covers
, 2003
"... A biclique B of a simple graph G is the edgeset of a complete bipartite (not necessarily induced) subgraph of G. A biclique cover of G is a collection of bicliques covering the edgeset of G. Given a graph G, we will study the following problem: find the minimum number of bicliques which cover the e ..."
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Cited by 3 (0 self)
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A biclique B of a simple graph G is the edgeset of a complete bipartite (not necessarily induced) subgraph of G. A biclique cover of G is a collection of bicliques covering the edgeset of G. Given a graph G, we will study the following problem: find the minimum number of bicliques which cover the edgeset of G. This problem will be called the minimum biclique cover problem (MBC). First, we will define the families of independent and dependent sets of the edgeset E of G: F ⊆ E will be called independent if there exists a biclique B ⊆ E such that F ⊆ B, and will be called dependent otherwise. From our study of minimal dependent sets we will derive a {0, 1} linear programming formulation of the following problem: find the maximum weighted biclique in a graph. This formulation may have an exponential number of constraints with respect to the number of nodes of G but we will prove that the continuous relaxation of this integer program can be solved in polynomial time. Finally we will also study continuous relaxation methods for the problem (MBC). This research was motivated by an open problem of Fishburn and Hammer.
Insensitive Traffic Splitting in Data Networks
, 2005
"... Bonald et al. have studied insensitivity in data networks assuming a fixed route for each flow class. If capacity allocation and routing are balanced and the capacity of a given class is shared equally between the flows, the network state distribution and flow level performance are insensitive to a ..."
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Cited by 3 (2 self)
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Bonald et al. have studied insensitivity in data networks assuming a fixed route for each flow class. If capacity allocation and routing are balanced and the capacity of a given class is shared equally between the flows, the network state distribution and flow level performance are insensitive to any detailed traffic characteristics except the traffic loads. In this paper, we consider optimal insensitive load balancing executed at packet level so that the traffic of each flow may be split over several routes. Similarly to the case with fixed routing, the most efficient capacity allocation and traffic splitting policy can be determined recursively. We formulate the problem as an LP problem using either a set of predefined routes or arbitrary routes and present numerical results for two toy networks. Traffic splitting gives a clear performance improvement when compared to flow level balancing or fixed shortest path routing.
Letters
, 2006
"... www.elsevier.com/locate/orl Polynomiality of sparsest cuts with fixed number of sources ..."
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www.elsevier.com/locate/orl Polynomiality of sparsest cuts with fixed number of sources
FlowCut Gaps for Integer and Fractional Multiflows
, 2010
"... Consider a routing problem instance consisting of a demand graph H = (V,E(H)) and a supply graph G = (V,E(G)). If the pair obeys the cut condition, then the flowcut gap for this instance is the minimum value C such that there exists a feasible multiflow for H if each edge of G is given capacity C. ..."
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Consider a routing problem instance consisting of a demand graph H = (V,E(H)) and a supply graph G = (V,E(G)). If the pair obeys the cut condition, then the flowcut gap for this instance is the minimum value C such that there exists a feasible multiflow for H if each edge of G is given capacity C. It is wellknown that the flowcut gap may be greater than 1 even in the case where G is the (seriesparallel) graph K2,3. In this paper we are primarily interested in the “integer ” flowcut gap. What is the minimum value C such that there exists a feasible integer valued multiflow for H if each edge of G is given capacity C? We formulate a conjecture that states that the integer flowcut gap is quantitatively related to the fractional flowcut gap. In particular this strengthens the wellknown conjecture that the flowcut gap in planar and minorfree graphs is O(1) [14] to suggest that the integer flowcut gap is O(1). We give several technical tools and results on nontrivial special classes of graphs to give evidence for the conjecture and further explore the “primal ” method for understanding flowcut gaps; this is in contrast to and orthogonal to the highly successful metric embeddings approach. Our results include the following: • Let G be obtained by seriesparallel operations starting from an edge st, and consider orienting all edges in G in the direction from s to t. A demand is compliant if its endpoints are joined by a directed